Approximation by interpolation trigonometric polynomials on classes of periodic analytic functions - Serdyuk, A. S. (Ukrains’kyi Matematychnyi Zhurnal, 2012)
We establish asymptotically unimprovable interpolation analogs of Lebesgue-type inequalities on the sets $C^{ψ}_{β}L_p$ of $(ψ, β)$-differentiable functions generated by sequences $ψ(k)$ that satisfy the d'Alembert conditions. We find asymptotic equalities for the least upper bounds of approximations by interpolation trigonometric polynomials on the classes $C^{ψ}_{β, p},\;\; 1 ≤ p ≤ ∞$.